Connectivity conjecture for the triangle-pseudoline incidence graph

A pseudoline arrangement is a finite collection of bi-infinite, simple curves in the Euclidean plane such that every pair crosses exactly once. A triangle-pseudoline incidence graph has as vertices the triangles and pseudolines of the arrangement, with an edge joining a pseudoline to each triangle it supports.

Triangle-pseudoline incidence graph conjecture. The triangle-pseudoline incidence graph of a pseudoline arrangement is connected.

The source notes that the original, weaker conjecture concerned projective arrangements. The status of the stated Euclidean version is not resolved in the supplied text.